Given:
The circumference of a circle is 18.
Central angle of an arc is 120 degrees.
To find:
The measure of arc length.
Solution:
The arc length of a circle is:
[tex]s=2\pi r\times \dfrac{\theta }{360^\circ}[/tex]
Where, r is the radius of the circle, [tex]\theta[/tex] is the central angle in degrees.
We know that, [tex]2\pi r[/tex] is the circumference of the circle. So, substitute [tex]2\pi r=18,\theta=120^\circ[/tex] in the above formula.
[tex]s=18\times \dfrac{120^\circ}{360^\circ}[/tex]
[tex]s=18\times \dfrac{1}{3}[/tex]
[tex]s=6[/tex]
Therefore, the length of the arc is 6 units.